Let be a closed surface, a compact Lie group, not necessarily connected, with Lie algebra , endowed with an adjoint action invariant scalar product, let be a principal -bundle, and pick a Riemannian metric and orientation on so that the corresponding Yang-Mills equations are defined.…
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48 results for “centrality stratification”
We revisit Atiyah and Bott's study of Morse theory for the Yang-Mills functional over a Riemann surface, and establish new formulas for the minimum codimension of a (non-semi-stable) stratum. These results yield the exact connectivity of the natural map (C_{min} E)//G(E) --> Map^E (M, BU(n)) from the homotopy orbits of…
Let be a closed surface, a compact Lie group, with Lie algebra , and a principal -bundle. In earlier work we have shown that the moduli space of central Yang- Mills connections, for appropriate additional data, is stratified by smooth symplectic manifolds and that the holonomy yie…
A model of multi-layer flow network explores international trade dynamics.
problem Analyzing multi-layer flow networks of international trade.
method Flow distances and symmetric minimum flow distance introduced; multi-layer flow network model proposed.
result Clustering patterns in trading 'trophic levels' are similar for different commodities; centrality stratification observed.
The paper characterizes and examines nilpotent complex structures on stratified Lie algebras.
problem Characterizing and understanding nilpotent complex structures on stratified Lie algebras.
method Introduced a new descending series to prove a new characterization of nilpotent complex structures and examined whether these structures preserve the strata.
result Found that there exists a -invariant stratification on a step 2 nilpotent Lie algebra with a complex structure.
We prove the existence of Verdier stratifications for sets definable in any o-minimal structure on (R, +, .). It is also shown that the Verdier condition (w) implies the Whitney condition (b) in o-minimal structures on (R, +, .). As a consequence the Whitney Stratification Theorem holds. The existence of (wf)-stratific…
The paper studies HKKN stratifications for non-compact spaces and proves convexity properties.
problem Proving convexity properties of moment maps for non-compact subsets.
method Algebraic and analytical study of HKKN stratifications for a vector space and compact Kähler manifold, then applying to non-compact subsets.
result Convexity properties of moment maps for invariant subsets are proven.
The paper defines a stratification for Lie groupoids in a tame topology context.
problem Presenting a tame topology counterpart to canonical stratification of Lie groupoids.
method Using Shiota's isotopy lemma and approximation theorem, the paper defines a canonical Whitney stratification of definable Lie groupoids into invariant strata.
result A canonical Whitney stratification of the Lie groupoid into definable strata invariant under the groupoid action.
Stratifies representation varieties of twisted Hopf links.
problem Stratifying representation varieties of twisted Hopf links.
method Using stratification of -representation varieties of the fundamental group of the complement of a twisted Hopf link.
result Explicit description and computation of motives for ranks 1 and 2.
Generalizes results for lambda-connections and Higgs bundles.
problem Understanding the Bialynicki-Birula stratification of lambda-connections.
method Analyzes the Bialynicki-Birula decomposition and its relation to Morse and partial oper stratifications.
result Fibers of the Morse and partial oper stratifications are transverse at the base point and are half-dimensional affine spaces.
MCS Spaces are CSmath.GT
Paper confirms MCS spaces are equivalent to CS sets.
problem Understanding the equivalence of MCS and CS sets.
method Analyzing the MCS stratification and intrinsic stratification.
result MCS spaces are equivalent to CS sets with respect to their stratification.
Alexandrov spaces have a special stratification that maps to spheres.
problem Characterizing the structure of Alexandrov spaces.
method Extremal stratification and space of directions analysis.
result Alexandrov spaces are homeomorphic to spheres in their space of directions.
Hidden Stratification Causes Clinically Meaningful Failures in Machine Learning for Medical Imagingcs.LG
Hidden stratification causes machine learning models to fail on rare but important patient subgroups.
problem Machine learning models fail on rare patient subgroups not identified during training or testing.
method Assessed techniques for measuring and describing hidden stratification effects on multiple medical imaging datasets.
result Evidence of hidden stratification leading to over 20% performance differences on clinically important subsets.
Investigates properties of moment maps and stratifications on Lie groups.
problem Understanding moment maps and stratifications on real reductive Lie groups.
method Functorial, algebraic approach to moment map and Kirwan-Ness stratification.
result Properties and properties of moment maps and stratifications established.
Optimizes biharmonic map regularity using stratification methods.
problem Improving the known almost optimal regularity of biharmonic maps.
method Quantitative stratification method.
result Optimal regularity results for minimizing biharmonic maps.
New stratification reveals intrinsic singularity types of orbit spaces.
problem Understanding the intrinsic structure of orbit spaces under Lie group actions.
method Introduced the isostabilizer decomposition and established a map to Klein strata.
result A new canonical stratification on the manifold clarifies the relationship with classical structures.
The monster tower's spaces are stratified naturally.
problem Describing the monster tower's spaces.
method Natural stratification of parameter spaces.
result A natural stratification of the monster tower's spaces.
On Arnold's notion of versal deformations and stratification of moduli spaces given by group actionsmath.GT
The aim of this paper is to compare stratifications of moduli spaces given by group actions in the case of similarity of matrices introduced by Arnold and the author's stratification by projective orbifolds, and its relation to deformations o elements in the moduli space.
Combines k-means and hill climbing for stratification and allocation.
problem Optimizing stratification and sample allocation for complex surveys.
method Combining k-means type algorithms with hill climbing.
result Multi-stage combination algorithms generally perform well compared to recent methods.
Social media enhances or diminishes scientific status, depending on usage.
problem Impact of social media on scientific stratification and mobility.
method Logistic Attribution Analysis combining statistical and machine learning methods.
result Social media promotes stratification and mobility, but beyond a threshold, it negatively impacts status.
Study clarifies variance of stratification estimators for causal effects.
problem Estimating average causal effects with discrete covariates.
method Combines insights from potential outcomes, causal diagrams, and structural models.
result Derives expressions for the variance of stratification estimators.
We give a geometric proof of existence of Whitney stratifications of definable sets in o-minimal structures.
This paper provides a stratification of semi-algebraic sets in the plane with finitely many geodesic segments.
problem How to stratify semi-algebraic sets in the plane with finitely many geodesic segments.
method Develops a semi-algebraic stratification of a real semi-algebraic set in the plane with open cells having the finiteness property.
result Provides insights for high-dimensional stratifications of semi-algebraic sets in connection with geodesics.
We study the topology of the inertia space of a smooth -manifold where is a compact Lie group. We construct an explicit Whitney stratification of the inertia space, demonstrating that the inertia space is a triangulable differentiable stratified space. In addition, we demonstrate a de Rham theorem for differ…
The paper stratifies projective measured laminations and identifies a group of transformations.
problem Stratifying the space of projective measured laminations.
method Introducing a natural stratification and proving rigidity results.
result The group of self-homeomorphisms preserving the stratification is identified with the extended mapping class group.
Study lifts Schubert stratification to , revealing new Bruhat cells.
problem Lifting Schubert stratification to .
method Explicit parameterizations of Bruhat cells using minimal-length permutations.
result Stratification of reveals new geometric structure.
The paper describes a stratification of a compactified Hurwitz space using combinatorial trees.
problem Describing the boundary stratification of a compactified Hurwitz space.
method Using decorated trees to describe the boundary strata and their containment relations.
result The boundary strata of the compactified Hurwitz space are in bijection with decorated trees, and containment is given by edge contraction.
The paper studies harmonic map flows and proves rectifiability of singular sets.
problem Understanding the structure of singular sets in harmonic map flows.
method Investigates the stratification theory for suitable solutions using tangent measures.
result Each time slice of the singular set is rectifiable.
The complement of a complex hyperplane arrangement is known to be homotopic to a minimal CW complex. There are several approaches to the minimality. In this paper, we restrict our attention to real two dimensional cases, and introduce the "dual" objects so called minimal stratifications. The strata are explicitly descr…
Let be a Lie group, and let be a symplectic manifold. If admits a Hamiltonian action on with momentum map , then , the zero-level set of , the orbit space, and the corresponding symplectic quotient all have induced stratifications. We push this setting into the language of differential …
ACDC algorithm creates a chain of decisions for risk stratification in healthcare.
problem Effective risk stratification in healthcare settings for resource allocation.
method Sequentially carves out 'pure' subsets of majority class examples to yield a pure subset of minority class examples.
result ACDC algorithm provides an interactive interpretation and visual performance metrics.
The paper offers simple, near-optimal algorithms for multi-group learning.
problem Learning predictors within subgroups of a population, addressing fairness and hidden stratification.
method Studies the structure of solutions and provides simple, near-optimal algorithms.
result Simple and near-optimal algorithms for multi-group learning.
Decomposes smooth manifolds into algebraic submanifolds.
problem Understanding the structure of smooth manifolds induced by continuous selections.
method Generic continuous selection of smooth functions provides stratification of the manifold.
result Stratification leads to local topological structure with nondegenerate critical points.
Dynamical thermalization and turbulence in social stratification modelscond-mat.stat-mech
Study chaotic dynamics in social stratification models leading to thermalization and turbulence.
problem Understanding social stratification dynamics through chaotic nonlinear systems.
method Modeling social network links with oscillators and energies, studying Hamiltonian evolution and nonlinear interactions.
result Chaotic dynamics leads to dynamical thermalization and Kolmogorov-Zakharov turbulence, with implications for wealth inequality.
Existence of closed geodesics proven on specific orbifolds.
problem Proving the existence of closed geodesics on compact developable orbifolds.
method Stratification of singular locus, reduction to even-dimensional orbifolds with specific properties.
result Existence of closed geodesics of positive length on compact developable orbifolds of dimensions 3, 5, or 7.
Study identifies and estimates treatment effect heterogeneity within principal stratification subpopulations.
problem Causal inference with intermediate outcomes and treatment effect heterogeneity.
method Proposes a novel doubly cross-fit doubly robust machine learner to efficiently learn conditional principal causal effects under principal ignorability.
result Demonstrates informative patterns of treatment effect heterogeneity within the always-survivor subpopulation in an acute lung injury trial.
Study almost rigidity of super Ricci flow with non-negative Muller quantity.
problem Almost rigidity properties of super Ricci flow with non-negative Muller quantity.
method Almost splitting and quantitative stratification theorems established by Bamler for Ricci flow.
result Obtained almost constancy for a certain integral quantity concerning scalar curvature at an almost self-similar point.
We consider a Morse function and a Morse-Smale gradient-like vector field on a compact connected oriented 3-manifold such that has only one critical point of index 3. Based on Laudenbach's ideas, we will show that the flow of can be isotoped into one so that the trajectory spaces of the new flow pro…
New method improves compatibility of risk stratification models without sacrificing accuracy.
problem Compatibility issues arise when updating clinical machine learning models.
method Proposes rank-based compatibility measure and new loss function.
result Increased compatibility of models by 0.019 with no loss in discriminative performance.
Study cohomology of abelian differentials, find new stratifications.
problem Cohomology classes in abelian differentials strata.
method Unified topological approach to find explicit stratifications.
result Explicit stratification of spin moduli space for odd spin structures.
A homology stratification is a filtered space with local homology groups constant on strata. Despite being used by Goresky and MacPherson [Intersection homology theory: II, Inventiones Mathematicae, 71 (1983) 77-129] in their proof of topological invariance of intersection homology, homology stratifications do not appe…
Deep Representation Learning of Electronic Health Records to Unlock Patient Stratification at Scaleq-bio.QM
Deep learning model creates patient representations for scalable EHR-based stratification.
problem Challenges in summarizing and representing patient data from EHRs prevent scalable stratification analysis.
method Unsupervised framework based on deep learning (ConvAE) using word embeddings, CNNs, and autoencoders.
result ConvAE significantly outperformed baselines in clustering diverse patient cohorts, identifying clinically relevant subtypes.
Survey on hyperplane arrangements and their topology.
problem Topology of hyperplane arrangements.
method Focus on the relationship between topology and real structure.
result Relationship between topology and real structure of hyperplane arrangements.
We reduce variance in monetization metrics for ranking experiments.
problem Heavy-tailed monetization metrics lead to unreliable conclusions in A/B experiments.
method Post-stratification combined with CUPED.
result Significant reduction in variance and improved decision stability.
Clarifies the structure of quantum states using algebraic methods.
problem Unclear stratification of quantum states in physics literature.
method Analyzes the state space S(A) of a finite-dimensional C*-algebra A, focusing on unitary orbits and their properties.
result Identifies a natural Whitney stratification of the state space into matrices of fixed rank, providing a pseudo-manifold structure.
The analysis of the USA 2001 income distribution shows that it can be described by at least two main components, which obey the generalized Tsallis statistics with different values of the q parameter. Theoretical calculations using the gas kinetics model with a distributed saving propensity factor and two ensembles rep…
We consider the problem of adaptive stratified sampling for Monte Carlo integration of a noisy function, given a finite budget n of noisy evaluations to the function. We tackle in this paper the problem of adapting to the function at the same time the number of samples into each stratum and the partition itself. More p…
Within its traditional range of perversity parameters, intersection cohomology is a topological invariant of pseudomanifolds. This is no longer true once one allows superperversities, in which case intersection cohomology may depend on the choice of the stratification by which it is defined. Topological invariance also…